Vibrational spectra of H2O and CF4 molecules using Lie algebraic approach

Abstract

In this paper, we introduce one dimensional vibron model to analyze the fundamental, overtone and combination modes of CF 4 molecule and both stretching , bending vibrational mode of bent H 2 O molecule up to first overtone with few algebraic parameters. Using the model Hamiltonian, we reported here better results for the vibrational spectra of H 2 O. Our analysis suggests some reassignments of levels and predicts location of states in case of CF 4 molecule which was not yet observed.

A Model Construction of Self-Similarity Based Double Parton Distribution Functions for Proton–proton Collision at LHC

“…and ν 0 (n), ν ± (n) are functions of n which are identified as anomalous dimensions and whose explicit forms are given in [27]. The above equations (Eq (18) and Eq (19)) show that the nth moment of quark/antiquark of any flavor transforms like…”

“…However, these ideas received wider attention in 2002 when Lastovicka [18] of DESY, Hamburg proposed a relevant formalism and a functional form of the structure function F 2 (x, Q 2 ) at small x based on self-similarity. In recent years, the present authors have applied the model to deep inelastic scattering [19], longitudinal structure function [20] and momentum fractions of quarks and gluons in the proton [21,22].…”

Vibrational Spectroscopy of H2O by Lie Algebraic Methods

“…The parameters λ ij describe the interactions between stretching bonds and the interaction between bending bond, respectively. The tting parameters [12] used in the study of vibrational spectra of water molecule are given in Table II. The highly excited vibrational levels, calculated by using the algebraic Hamiltonian Eq.…”

“…The main features and basic applications of these methods have been described by Iachello and Levine [11] and Oss. The Lie algebraic approach was found to be successful in our study of the vibrational spectra of H 2 O and CF 4 [12], HCN [13], HCCF, HCCD [14], tetrahedral [15], nickel metalloporphrins [16], copper tetramesityl porphyrin [17]. Highly accurate prediction of molecular vibrations has been a challenging task since ever in theoretical and physical chemistry.…”

Studies of the Vibrational Energy Level of H2O by Algebraic and DFT Approaches

“…The brief review of the research work done with the algebraic models up to the year 2000 and its outlook and perception in the first decade of the 21st century were presented by Iachello and Oss. Recently, it is found that the Lie algebraic method [6][7][8][9][10] is extremely successful and accurate in calculating the vibrational frequencies of polyatomic molecules as compare with the other methods such as the Dunham expansion and the potential approach method reported earlier [11]. As a specific complementary technique to the conventional approaches, the algebraic approach has already proved to be successful in the study of molecular spectra during the last 29 years.…”